Question

1 If u = x2 + y2 +7, v = x + y + z, w = x y + y z + z x, show that the Jacobian
(u, v, w)
vanishes identically. Find also the relation between u, v and w.
a(x, y, z)​

Answer 1

v + 1 and v ≡. 1 u − 1. − 1. 2. If u ≡ x + y and v ≡ x2 + 2xy + y2, then ... Two functions, u(x, y) and v(x, y), are independent if and only if ... u ≡ u(x, y, z), v ≡ v(x, y, z) and w ≡ w(x, y, z).